Merge UV vertex across islands?
Select all your UVs, hit W and choose Remove Doubles. You can set a threshold distance that should take care of the overlaps. Be careful though, if you have small islands, or large overlaps, it will merge the wrong vertices, so keep the distance as small as possible. Rather do a couple by hand than risking wrongfully merged UVs, because they might be a pain to spot and to fix.
EDIT:
Merging does not work, bc those UV vertices are not doubles. Each triangle seems to be rotated or flipped:

So adjacent vertices on the UV map are not (necessarily) adjacent in your mesh. I'm afraid that thing is busted beyond repair, meaning there was an issue importing the coordinates. Where did the model come from and wich format was it?